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Problems in Teaching Primary School Mathematics
Seán Delaney, PhD Marino Institute of Education
Laois Education Centre
18 October 2012
Introductions
Who here: • Teaches junior/senior infants • Teaches 1st/2nd class • Teaches 3rd/4th class • Teaches 5th/6th class • Teaches a single class level • Teaches two class levels • Teaches three or more class levels • Teaches in a DEIS school • Is a learning support teacher • Is a resource teacher • Is a principal
What’s on your mind about teaching mathematics?
• Language of mathematics – reading problems can be tough • How to make problem solving fun – children’s faces drop when
they’re doing the SIGMA (especially children with special needs) • Link between primary school maths and Junior Cert Project Maths
– what is worth emphasising in senior classes? • Recommend any good maths games? • Ideas for use of interactive boards in maths class • Use of hands-on materials in senior classes – when you could have
30+ in the class • Creating a maths-friendly environment in the school - changing it • Preparing for a WSE in relation to maths • Challenging “brighter” children
How will this evening help you?
New habits change practice
Choose one maths teaching habit that you can adopt based on this evening’s presentation and from discussion before during and after
the presentation
Plan for Presentation
• Key element in improving the teaching of maths
• My story in teaching maths
• An example of teaching maths to promote children’s thinking
• Teaching maths using problems
• Finding and choosing problems
• The problem of differentiation in maths class
A key element in improving the teaching of maths is ...
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...NOT
BUT... www.seandelaney.com
...getting children to think and talk mathematically
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Encourage Teachers to ask questions such as...
Compare
Estimate
How does that connect with…?
www.seandelaney.com
How can you tell...?
Encourage Teachers to ask questions such as...
Compare
Estimate
How does that connect with…?
www.seandelaney.com
How can you tell...?
How I taught maths
• Check the children’s homework or do a tables or mental maths activity
• Demonstrate how to do some sample problems by doing them on the board
• Ask the children to practise problems similar to those for which solutions were demonstrated. Give individual help to children who were having difficulties.
• Correct class work and assign homework
Why I began to teach maths differently
2 6 - 1 7
Video
If children only learn to memorise, they give up thinking for themselves
There are other ways to teach A
Review homework or remind children of accomplishments so far Present the topic and problems for the day Students or teachers develop procedures to solve the problem(s) at the board, taking suggestions from other students and the teacher Practise doing problems similar to those worked on above
B Review the previous lesson with a brief teacher lecture or summary by students Present the problem for the day. One problem only. Students work individually on problems first and then in groups for 5-10 minutes Students (selected by teacher) present and discuss one or more solution methods. Highlight and summarise major points
C Review previous material: Check homework or engage in warm-up activity Demonstrate how to solve problems for the day by presenting a few sample problems and demonstrating how to solve them Practise problems similar to those for which solutions were demonstrated Correct class work and assign homework
GERMANY JAPAN UNITED STATES
How I try to teach maths now
• Much more talking about maths in the classroom
• Children share their ideas with each other
• Get the children reasoning and justifying their answers
• Use fewer problems
• Use more open-ended problems
• Use the problems to teach a new maths topic, not just to check if the children understand it
Sample Open-ended Problem
Dublin Zoo has just received two new sheep for the Family Farm part of the zoo. The zoo keeper wants to build an enclosure for the sheep. She decides that the enclosure must be square or rectangular with an area of 100 square metres. 1. Which different configurations could she build? 2. How many metres of fencing will she need for each possible
design? 3. Use your copy or some graph paper to draw all the possible
rectangular or square designs. 4. Include a key to tell how much each unit on the grid paper
equals. 5. Which fence would you recommend that the zoo keeper
builds? Why?
Sample of Teaching Using Problems
• Video Clip • 20 Fifth class children • Recruited from 11 different schools (4 DEIS),
mostly around Marino area • Topic: Area • After school on a Friday afternoon in May 2011 • Maths Laboratory: Goal is not to offer model
teaching, but public teaching • Observed by 20 educators • Amplified and video recorded
Link to Video Time-Code 04, from 12’31’01” to 16’56” (or earlier)
Problem Solving Strategy 1
RUDE
• Read the problem
• Underline the key words
• Draw a diagram of the problem
• Estimate your answer and then solve the problem
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Problem Solving Strategy 2
STAR
• Search the word problem (info)
• Translate the words into an equation or picture (plan)
• Answer the problem (solve)
• Review the solution (check)
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Problem Solving Strategy 3
LUV2C
• Look
• Underline
• Visualise
• Choose Numbers
• Calculate
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Teaching Mathematics Using Problems
• Little evidence that such strategies work
• Some evidence that classifying problems into problem-types can be helpful for children with learning disabilities
• Best way to learn problem solving is to practise solving problems
• Skill in problem solving develops slowly over time
• Many textbooks have too many problems, and many of the problems are of poor quality
Worked Example in a Textbook from Taiwan
www.seandelaney.com From Charalambous et al, 2010
Worked Examples in 2 Textbooks from Ireland
www.seandelaney.com From Charalambous et al, 2010
Sources of Problems
• http://nrich.maths.org/frontpage
• http://www.nctm.org/ (Annual subscription necessary)
Choosing a Problem
A good problem...
• Should leave the solver feeling “stuck” at first
• The maths is what makes the problem problematic
• Relates to the children’s experience
• Connects different maths topics
• Allows children with different attainment levels to achieve success with it
• May take time, even days, to complete
• Requires children to justify and explain their answers and methods
The problem of differentiation in teaching maths
Children differ in many ways • Within maths (from strand to strand) • Within maths skills • How they learn • Motivation • Learning disabilities • Giftedness Generic labels, such as weak, bright, lazy, clever,
etc., can disguise children’s specific talents and shortcomings
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Differentiation Strategies
• Encourage all children to work together to help the class as a whole to learn maths – learning maths through talking through ideas
• Use problems that children can approach at different levels
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Sample Problem for Differentiation
I have 10-cent, 5-cent and 1-cent coins in my money box. If I open the box and take out three coins, how much money could I have? How can you be sure that you have found all the possible amounts?
Skills Children Need in Order to Succeed in Maths
• Conceptual processing (e.g. identifying and extending patterns)
• Language (e.g. reading a word problem) • Visual-spatial processing (e.g. working with 2-d and 3-d
representations) • Organisation (e.g. collecting and recording data) • Memory (e.g. remembering number facts; remembering
the steps of a mathematical procedure) • Attention (e.g. focusing on the details in a maths problem) • Psycho-social (e.g. working with a partner or in a group) • Fine-motor skills (e.g. drawing geometric figures)
(Brodesky, 2002)
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A child with dyslexia Possible Learner Difficulties
Possible Teacher Response
Language comprehension impairment
Use vocabulary that is familiar to the student Explain new vocabulary carefully Monitor and vary the level of text learners are expected to read in mathematics problems Highlight words that have different meanings in different contexts (e.g. third, prime, factor)
Counting speed is slower than
in other learners
Provide more time in tables and other maths tests to allow students to use
strategies when they can’t recall number facts
Memory problems Give short instructions Recap at end of lesson and revisit topics frequently Monitor early work on new topics carefully so that incorrect strategies are not practised Use concrete materials (including fingers or pictures)
Omission of digits and numerals
Encourage learners to compare answers with estimates
Directional confusion in writing digits and doing algorithms
Work on the concepts first and on recording later
A Child with dyslexia
Possible Learner Strengths
Estimation
Subitising
Place value
Possible Learner Difficulties
Possible Teacher Response
Phonological (speech sounds) processing
Exaggerate differences in words that sound similar (e.g. Tens and tenths; hundreds and hundredths; fifteen and fifty)
Difficulty with the decimal
place
Highlight the decimal point – possibly by recording it in a different colour
Supplementary Material
Concrete Materials & Visual Aids
• Base Ten Materials
• Geoboards
• Rulers
• Hundred Square
• Addition Table
• Multiplication Table
Base Ten Materials
Naming Them
• Small cubes
• Longs
• Flats
• Large Cubes
Uses of Base Ten Materials
• Estimate how many small cubes on the table
• Equivalent Representations
• Demonstrating addition, subtraction and division
• Introducing Decimals (Re-define the unit)
Geoboards
http://www.ordinarylifemagic.com/2010/06/geoboard-games.html
Uses of Geoboards
• Angles
• Symmetry
• Percentages
• Fractions
• 2-D Shapes
• Area and perimeter
Rulers or Measuring Tapes
Uses of Rulers
• Number lines
• Measuring
• Fractions and decimals
Addition and Multiplication Number Facts
ADDITION
NUMBER
FACTS IN
FIRST CLASS
Start with a
blank 12x12
grid
Show the
children how
the addition
square works
by giving
some
examples
e.g. 1+
+ 0 1 2 3 4 5 6 7 8 9 10
0 1
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10
10 11
Or 6+
+ 0 1 2 3 4 5 6 7 8 9 10
0 6
1 7
2 8
3 9
4 10
5 11
6 12
7 13
8 14
9 15
10 16
BUILD UP
THE REST
OF THE
ADDITION
SQUARE
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
MAKE THE
ADDITION
FACTS EASIER
BY
ELIMINATING
THE …
COMMUTATIVE PAIRS
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE +0 FACTS
0+0
1+0
2+0
3+0
4+0
5+0
6+0
7+0
8+0
9+0
10+0
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE +1 FACTS
1+1
2+1
3+1
4+1
5+1
6+1
7+1
8+1
9+1
10+1
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE +2 FACTS
2+2
3+2
4+2
5+2
6+2
7+2
8+2
9+2
10+2
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE TEN AND
FACTS
10+3
10+4
10+5
10+6
10+7
10+8
10+9
10+10
…THE
DOUBLES
3+3
4+4
5+5
6+6
7+7
8+8
9+9
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE NEAR
DOUBLES
3+4
4+5
5+6
6+7
7+8
8+9
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE TEN AND
NINE FACTS
AND FIVE AND
FACTS
6+4
7+3
6+3
5+3
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
…THE
THROUGH TEN
FACTS
7+4
7+5
8+3
8+4
8+5
8+6
9+3
9+4
9+5
9+6
9+7
+ 0 1 2 3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10 11
2 2 3 4 5 6 7 8 9 10 11 12
3 3 4 5 6 7 8 9 10 11 12 13
4 4 5 6 7 8 9 10 11 12 13 14
5 5 6 7 8 9 10 11 12 13 14 15
6 6 7 8 9 10 11 12 13 14 15 16
7 7 8 9 10 11 12 13 14 15 16 17
8 8 9 10 11 12 13 14 15 16 17 18
9 9 10 11 12 13 14 15 16 17 18 19
10 10 11 12 13 14 15 16 17 18 19 20
Multiplication
MULTIPLICA
TION
NUMBER
FACTS IN
THIRD
CLASS
Start with a
blank 12x12
grid
x 0 1 2 3 4 5 6 7 8 9 10
0 0
1 3
2 6
3 9
4 12
5 15
6 18
7 21
8 24
9 27
10 30
SHOW THE
CHILDREN
HOW IT
WORKS BY
GIVING
SOME
EXAMPLES
Eg. 3x
x 0 1 2 3 4 5 6 7 8 9 10
0 0
1 6
2 12
3 18
4 24
5 30
6 36
7 42
8 48
9 54
10 60
SHOW THE
CHILDREN
HOW IT
WORKS BY
GIVING
SOME
EXAMPLES
Eg. 6x
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
BUILD UP
THE REST
OF THE
MULTIPLI-
CATION
TABLE
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
COMMUT-
ATIVE
PAIRS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
ZERO
FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
ONE FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
TEN FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
TWO FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
FIVE FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
NINE
FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
FOUR
FACTS
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
PROMOTE
UNDER-
STANDING
OF MULTI-
PLICATION
FACTS BY
POINTING
OUT:
THREE
FACTS
(2 TIMES,
ADD ONE
MORE)
x 0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 0 9 18 27 36 45 54 63 72 81 90
10 0 10 20 30 40 50 60 70 80 90 100
SIX, SEVEN
AND EIGHT
FACTS
REMAIN.
Abstract
In this session Seán Delaney will discuss the use of problems in mathematics teaching in primary classrooms (2nd to 6th class). Topics covered will include approaches to teaching mathematics using problems, differentiation using problems, teaching maths skills using problems, and choosing problems. Questions and discussion about mathematics teaching are welcome.
